Solve 3(b-a)-2(a-b)^2

$$3 ( b - a ) - 2 ( a - b ) ^ { 2 }$$

Evaluate

$$\left(a-b\right)\left(-2a+2b-3\right)$$

Solution Steps

Use the distributive property to multiply 3 by b-a.

$$3b-3a-2\left(a-b\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

$$3b-3a-2\left(a^{2}-2ab+b^{2}\right)$$

Use the distributive property to multiply -2 by a^{2}-2ab+b^{2}.

$$3b-3a-2a^{2}+4ab-2b^{2}$$

Expand

$$3b-2b^{2}-3a+4ab-2a^{2}$$

Solution Steps

Use the distributive property to multiply 3 by b-a.

$$3b-3a-2\left(a-b\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

$$3b-3a-2\left(a^{2}-2ab+b^{2}\right)$$

Use the distributive property to multiply -2 by a^{2}-2ab+b^{2}.

$$3b-3a-2a^{2}+4ab-2b^{2}$$